How To Win With Math

Every day, we make decisions based on what we think may, or most likely will, happen. Many of these decisions seem to be based more on wishful thinking than on logic - sure, you'll run off that extra banana split! No, of course you won't get a parking ticket in the course of a five-minute stop! But nowhere can we see more of these hopeful, if not necessarily logical, guesses about the future than in gambling and betting.

From the stock market to the office betting pool, from the political futures market to the casino, from the street-corner game of three-card monte to a familial round of poker, we all act as if we believe that winning is always a possibility. But what so many of us don't know is that mathematics offers an entire body of research, speculation and solid fact dedicated to helping us predict the future.

With probability, as this field of mathematical inquiry is called, we can make more educated guesses as to the likeliest outcome of a given event. (Probability's applicability to games of chance is no accident, either - mathematicians began studying it in seventeenth-century France partly in order to understand how such games worked, since they were an important pastime among the very aristocratic patrons who performed or funded math research and other intellectual pursuits.)

The simplest way to figure probability is as a fraction. Let's say someone dares you to reach into a box filled with four real dollar bills and five fakes. In this case, the likelihood of getting a dollar bill on your first grab is 4/9 - four out of nine (the ratio of real dollar bills to the total number of items in the box). You could also express this probability as a percentage - just divide 4 by 5. You get around forty-four percent - not terrible. Why not take the risk, especially since you're not losing anything?

Now let's make the problem a little harder - figuring the outcome of a coin toss. Being able to "call" heads or tails may not seem like a very important skill in the scheme of things, but it never hurts' and you never know.

Viewers of the popular recent movie No Country For Old Men will recall the frightening scene in which bad guy/hitman Anton Chigurh, played brilliantly by Javier Bardem, stalks into a remote Texas gas station and offers to let the proprietor live - if he "calls" a coin toss correctly. "What's the most you've ever lost on a coin toss?" Chigurh says, mocking the terrified man. In other words - sometimes it pays to know a little probability!

So let's say you've been asked to call a coin toss - hopefully not by a madman with a gun. If it's a single coin toss, the result is pretty simple to figure: you can either call heads or tails, and the probability that the coin will agree with you is, basically, 1/2, with two being the number of possible results (heads, tails). That yields a probability, of course, of fifty percent. Not bad. Might as well call it, friend-o.

Your chances at the roulette wheel, however, aren't quite so good. And the reason, again, has to do with probability. On a roulette wheel, you have 38 slots: two green, 18 red, and 18 black. Let's say you bet simply on "red" - a hedged bet, with a correspondingly lower payout. Your chances of winning are 18 out of 38. That yields a not-too-terrible forty-seven percent chance.

If you play for the real money - placing your bet on, say, red-ten - your chances plummet to 1 in 38, or a little less than three percent. Suddenly we can see how casino owners manage to afford to stay in business. These are, of course, incredibly simple applications of - and examples of - probability.

Scientists use probability to study everything from political events (the likelihoods of assassination and coup attempts), to the possibility of Earth-like planets existing at various points in the galaxy. Insurance agencies use probability in order to anticipate risk; economists and investors use it to make guesses about stock performance and other variables.

Mathematicians have even used probability to study the effect of peoples' assumptions about the probability of certain events - for example, how does cynicism about the market contribute to economic downturn? How do fears of further Middle East conflict affect oil prices? Probability may be as simple as a coin toss - but it's as complicated as existence.